3D Discontinuous Deformation Analysis Research Articles

Extension of a 3D Geological Entity Modeling Method for Discontinuous Deformation Analysis

AbstractWith the development of 3D discontinuous deformation analysis (DDA) in precise stress fields and crack propagation problems, it has also demonstrated outstanding capabilities in solving continuous–discontinuous problems. However, currently, 3D DDA modeling primarily focuses on generating rock joint networks and developing 3D cutting algorithms. Correspondingly, 3D geological modeling methods are not yet mature, and establishing 3D models often demands substantial time. The lack of supporting preprocessing modeling methods and corresponding visual operation interfaces significantly hampers the development of 3D DDA. This method builds upon advanced research achievements in unmanned aerial vehicle oblique photography, 3D reconstruction, 3D cutting, computer graphics, and visualization program design. This research establishes a 3D geological entity modeling method for 3D DDA and constructs a comprehensive program using relevant C++ libraries and C language interfaces. In this method, a 3D geological model that incorporates geological elements such as strata and faults is initially established using non‐uniform rational B‐splines (NURBSs) surfaces as the boundary of the solid model. Subsequently, finite element meshing is applied, followed by corresponding topology transformation, resulting in a 3D block system model suitable for 3D DDA calculation. To cater for diverse application scenarios, continuous–discontinuous models integrated with subblocks and models of arbitrary polyhedra can be established. The proposed method has been validated through several typical modeling examples, showing its ability to rapidly and generate 3D high‐precision geological reality models suitable for 3D DDA calculations. Additionally, some techniques used in this method can be extended for modeling other numerical simulation methods, warranting further research.

Modeling the failure process of rock masses using a 3D nodal-based continuous-discontinuous deformation analysis method

A three-dimensional nodal-based continuous-discontinuous deformation analysis method (3D-NCDDAM) is developed in this study for modeling the failure process of rock masses. In the 3D-NCDDAM, four-node tetrahedral elements which can be automatally generated are used to discretize the problem domain. To reduce computational cost, and effectively model the failure process of rock masses at concerned regions, the problem domain is devided into two types of regions, namely, the “non-destructive region” and “possible destructive region”. The non-destructive region is mainly used to reduce the boundary effects on the numerical results, and is regarded transitional zone in which the failure of rock masses is not considered. For the possible destructive region, artificial joint elements are inserted, and the failure of these joint elements is used to represent fracture initiation and propagation in rock masses. Additionally, the contact potential which is initially proposed in finite-discrete element method (FDEM) is incorporated into the 3D-NCDDAM to simuate the opening and slipping of discontinuous structural planes involved in rock masses’ failure process. Note that the difficultly in determing contact types in the traditional 3D discontinuous deformation analysis (3D-DDA) method is avoided in the 3D-NCDDAM. The proposed 3D-NCDDAM can be treated as a hybrid method, which inherite both the advantage of DDA method and FDEM. To validate the 3D-NCDDAM, seven numerical examples are conducted. The numerical results indicte that the 3D-NCDDAM can effectively model the failure process of rock masses in both experimental scale and engineering scale.

An extended 3D discontinuous deformation analysis method considering bolt supports and its application in tunnels

Implementing bolt supports is the main means of controlling block instability. However, the original three-dimensional discontinuous deformation analysis method (3D ODDA) is still unable to simulate bolt supports, making it difficult to study the control effect of bolt supports on block instabilities. Therefore, an extended three-dimensional discontinuous deformation analysis method (3D EDDA) that can simulate the effect of bolt supports is proposed in this article. Based on the 3D ODDA method, we proposed a simulation algorithm for bolt supports, which improves the constitutive model of the bolt in the original DDA method. Then, we analysed the failure process of a bolt between two blocks and compared the numerical simulation results with the theoretical analysis results to verify the accuracy of the bolt support algorithm in the 3D EDDA method. With the 3D EDDA method, we simulated the failure process of the surrounding rock in a jointed rock mass tunnel at the engineering scale under conditions with bolt supports and without bolt supports. By comparing the results of these two conditions, we deduced the evolution law of the block displacement and bolt axial force around the tunnel and determined the anisotropic characteristics of these items. Specifically, the axial force of the local bolts is relatively small and has a small control effect on the stability of the block in the area. During actual construction, the length or strength of these bolts can be reduced, which can provide a theoretical basis for the design of tunnel bolt support parameters.

Development of a Composite Implicit Time Integration Scheme for Three-Dimensional Discontinuous Deformation Analysis

Discontinuous deformation analysis (DDA) is a discontinuum-based and implicit method for investigating the deformational behavior of block systems. The constant acceleration integration (CAI) scheme characterized by unconditional stability is employed in the traditional DDA. In this study, the problems of the CAI scheme regarding the time step in DDA are pointed out. A too large or too small time step size adopted in the CAI scheme will have adverse effects on the DDA computation. To overcome the weaknesses, an alternative composite implicit time integration (CITI) scheme, which is a combination of the trapezoidal rule and the three-point backward Euler method, is implemented in the three-dimensional (3D) DDA method. Verification examples and slope numerical simulations are presented to illustrate the accuracy and effectiveness of the proposed methodology. The results showed that the CITI scheme can overcome the numerical error caused by the large time step size, and the algorithm damping is closely related to the time step size and the selected splitting parameter.

A Nodal-Based 3D Discontinuous Deformation Analysis Method with Contact Potential for Discrete Rock Block System

A Nodal-Based 3D Discontinuous Deformation Analysis Method with Contact Potential for Discrete Rock Block System

Motion characteristics of rockfall by combining field experiments and 3D discontinuous deformation analysis

Rockfall is a common geological disaster in rock slope projects. An understanding of the motion processes and characteristics of the rock blocks originating from a rockfall is of profound importance for comprehending the mechanism(s) of rockfall disasters. In this study, a field experimental system comprising binocular stereovision was developed for examining rockfalls, and a series of experiments on rockfall motion characteristics were performed on slopes near an abandoned section of the G318 national highway in Tibet, China. The indices of motion characteristics such as the lateral displacement, staying position, jumping height, and kinetic energy evolution of the blocks under different work conditions (e.g. different masses, shapes, falling heights, falling angles, and different geometrical characteristics in the slopes) were investigated by combining experiments with a three-dimensional discontinuous deformation analysis (3D DDA) method. The results show that the field experimental system has high accuracy in monitoring the block movement processes. The 3D DDA results agree well with those from the experiments, and the evolutions of the motion characteristics of the rockfall under different conditions are quantitatively obtained. Furthermore, the results provide insight into the laws of rockfall movements and dynamic impact processes, and lay a foundation for the design of rockfall protection measures and engineering approaches for disaster prevention and mitigation.

Kinetic analysis of polyhedral block system using an improved potential-based penalty function approach for explicit discontinuous deformation analysis

The complexity of polyhedral block systems (e.g., small blocks, flat blocks with small angles, edges, or faces) poses challenges in the kinetic analysis of rock block systems. This paper proposed an improved potential-based penalty function approach within an explicit three-dimensional (3D) discontinuous deformation analysis (DDA) framework for efficient and robust kinetic analysis of rock block systems. An explicit formulation of 3D DDA based on velocity verlet algorithm is first derived. A novel definition of potential function is then proposed with details of the key algorithms for overlap judgment of convex polyhedron, construction of intersection polyhedron and numerical integral for computation of contact force. The improved potential-based penalty function method is robust and efficient for complex convex polyhedral shapes. Several benchmark and application examples verify the feasibility, accuracy and robustness of the proposed methods in solving contact of polyhedral block systems.

Failure Mechanisms of Toppling Rock Slopes Using a Three-Dimensional Discontinuous Deformation Analysis Method

Toppling is a representative failure mode of discontinuity-controlled rock slopes. As a discrete numerical method, discontinuous deformation analysis (DDA) is well-suited for simulating the movement process, contact transformation, and large displacement and deformation of rock block systems, which are formed in jointed rock masses. In the present study, a three-dimensional (3D) DDA method was conducted to study the toppling failure mechanisms of rock slopes by introducing the global contact theory. Considering dynamic equilibrium conditions, the analyses of toppling slopes were performed and the corresponding formulations were derived. The algebraic and mechanical computation of the global contact theory was illustrated and implemented into the 3D DDA method. An experimental apparatus for studying the toppling process of blocks was developed and a series of laboratory experiments were carried out for different block distributions under different conditions. By comparing with the results of the analytical methods and laboratory experiments, the accuracy of the 3D DDA method was verified. Numerical examples, including a classical toppling slope, an ideal mountain slope, and a real toppling case were analyzed to further research the toppling failure mechanisms. The results revealed that the 3D DDA method can effectively predict slope instability and simulate the failure process of toppling slopes. The results of the dynamics-based formulations, experiments and 3D DDA enrich the instability conditions of slope-toppling. Moreover, the general phenomena and laws of the toppling failure were presented.

3D DDA Based on Variational Inequality Theory and Its Solution Scheme

The advantage of 3D discontinuous deformation analysis (3D DDA) is the rigorous contact conditions on the interaction of 3D blocks. These conditions are enforced by the penalty function convention; however, inappropriate penalty parameters easily generate numerical instability. To avoid the introduction of the penalty parameters, the contact conditions in 3D DDA are described as variational inequalities in this study, and the extra-gradient method is employed to solve this new formulation of 3D DDA. The proposed computation scheme is more flexible and dispenses with large scale matrix inversion. Some practical examples originally designed by Shi are analysed, verifying the effectiveness and precision of the new scheme.

Numerical comparison of some contact detection algorithms

PurposeContact interaction and contact detection (CD) remain key components of any discontinua simulations. The methods of discontinua include combined finite-discrete element method (FDEM), discrete element method, molecular dynamics, etc. In recent years, a number of CD algorithms have been developed, such as Munjiza–Rougier (MR), Munjiza–Rougier–Schiava (MR-S), Munjiza-No Binary Search (NBS), Balanced Binary Tree Schiava (BBTS), 3D Discontinuous Deformation Analysis and many others. This work aims to conduct a numerical comparison of certain algorithms often used in FDEM for bodies of the same size. These include MR, MR-S, NBS and BBTS algorithms.Design/methodology/approachComputational simulations were used in this work.FindingsIn discrete element simulations where particles are introduced randomly or in which the relative position between particles is constantly changing, the MR and MR-S algorithms present an advantage in terms of CD times.Originality/valueThis paper presents a detailed comparison between CD algorithms. The comparisons are performed for problem cases with different lattices and distributions of particles in discrete element simulations. The comparison includes algorithms that have not been evaluated between them. Also, two new algorithms are presented in the paper, MR-S and BBTS.

Three-Dimensional Spherical DDA Method for Modeling Friction Problems

AbstractThree-dimensional (3D) discontinuous deformation analysis (DDA) is very suitable for simulating large-displacement behavior of rock masses. One fundamental issue commonly encountered in 3D DDA is 3D friction problems. In this paper, a friction contact model based on 3D spherical DDA (SDDA) and the determination method of friction force direction is proposed for modeling 3D friction problems. Simulation results of three verification examples with available analytical solutions demonstrate the correctness of the friction contact model in 3D SDDA. Meanwhile, the simulation result of one application example, namely, a 3D-sphere natural-accumulation simulation, indicates that the friction problems of a 3D-sphere system can be modeled well by the proposed friction contact model. This work is helpful for solving 3D friction problems in discrete blocky systems.

A new approach for modeling landslide movement over 3D topography using 3D discontinuous deformation analysis

Landslide movement analysis over three-dimensional (3D) topography is crucial for hazard evaluation and prevention. This paper presents a new approach to simulate landslide movement considering the 3D spatial effects of both the landslide mass and topography using discontinuous deformation analysis (DDA). The approach involves two aspects: the ordered blocky topography (OBT) treatment for the base slope and an algorithm for fast contact detection between the landslide block (LB) and the OBT. By introducing the OBT treatment, the LB-OBT contact detection can be simplified from the global range to the local sub-topography using the current algorithm, which enhances the computation efficiency. The approach has been implemented in the 3D-DDA program. Finally, the capability and performance of the proposed approach for landslide movement modeling were well demonstrated by two numerical examples.

NEW CONTACT-DEFINITION ALGORITHM USING INSCRIBED SPHERES FOR 3D DISCONTINUOUS DEFORMATION ANALYSIS

The speed and stability of three-dimensional (3D) discontinuous deformation analysis (DDA) are strongly dependent on the efficiency and correctness of contact detection and the definition algorithm, which affects the simultaneous equilibrium equations solved in every open–close iteration (OCI) retry. In particular, the definition of vertex-to-vertex contacts in a tangled zone may abruptly change the entrance planes, even in the case of very small displacement of the objects. This study proposes a new contact-definition algorithm using an inscribed sphere virtually installed in every contacting vertex. The suggested algorithm generates virtual entrance planes in the case of a vertex-to-vertex contact, and controls the accuracy of the contact definition process by adjusting the sphere size. Verification tests of the proposed algorithm indicate an increase in the efficiency and stability of 3D DDA.

Improvement of contact detection in 'approaching faces' method for use in three-dimensional discontinuous deformation analysis

One of the most efficient procedures of contact detection in three-dimensional distinct element method (3D DEM) is detection of contact patterns between approaching faces of two neighbouring convex blocks, however some modifications should be done on this method to make it usable in 3D discontinuous deformation analysis (DDA). In many occasions two blocks having more than one pair of approaching face come close to each other. Consequently, more than one contact pattern may be detected which results in multicalculation of some contact points and following incorrect calculation of contact forces in 3D DDA. By applying the algorithm of 'dominant contact detection' presented in the present paper, only one contact type which includes all contact points is found among all detected contact patterns. The proposed algorithm was programmed using VC++ and verified by an illustrative example.

Theory of Three-Dimensional Discontinuous Deformation Analysis and Its Application to a Slope Toppling at Amatoribashi, Japan

A three-dimensional (3D) rock slope toppling occurred in a discontinuous rock mass. To simulate the failure process and study the mechanism of this rock failure with contact and large displacement in 3D, a new discrete numerical method has been developed called the 3D discontinuous deformation analysis (DDA). This article first introduces the basic principles and then derives the formulas in detail. Finally, the slope failure simulation is applied as an example to investigate the applicability of this new method to rock slope failure research. The simulation results indicate the advantages of using this new method to study the mechanism of a rock slope failure with 3D behavior.

Numerical analysis of discontinuous rock masses using three-dimensional discontinuous deformation analysis (3D DDA)

Numerical analysis methods are considered very important in the field of geotechnical engineering, particularly in the area of disaster prevention. Discontinuous Deformation Analysis (DDA) is a type of discontinuous numerical analysis method that is frequently used in this topic. Since most geotechnical engineering problems are three-dimensional, Two-Dimensional Discontinuous Deformation Analysis (2D DDA) computations have exhibited limited accuracy. In order to simulate three-dimensional block behavior more accurately, the Three-Dimensional Discontinuous Deformation Analysis (3D DDA) theory for blocks with general shape was developed. This paper describes the basic principles of 3D DDA, and goes a step further by developing a new 3D DDA method. This new 3D DDA method proposed by authors is applied to an actual example site. In order to demonstrate the capability of this new method in the numerical analysis of discontinuous rock masses, the simulation results were compared and examined with the actual monitoring of the displacement behavior proceeding that led to the failure at the field site. The results show the applicability of 3D DDA in determining the deformation and failure mechanisms of rock masses.

Formulations of the three-dimensional discontinuous deformation analysis method

This paper extends the original 2D discontinuous deformation analysis (DDA) method proposed by Shi to 3D cases, and presents the formulations of the 3D DDA. The formulations maintain the characteristics of the original 2D DDA approach. Contacts between the blocks are detected by using Common-Plane (C-P) approach and the non-smooth contact, such as of vertex-to-vertex, vertex-to-edge and edge-to-edge types, can be handled easily based on the C-P method. The matrices of equilibrium equations have been given in detail for programming purposes. TheC program codes for the 3D DDA are developed. The ability and accuracy of the formulations and the program are verified by the analytical solutions of several dynamic examples. The robustness and versatility of the algorithms presented in this paper are demonstrated with the aid of an example of scattering of densely packed cubes. Finally, implications and future extensions are discussed.